Sex differences in weight gain (original Lord formulation)

Variables

  • weight time 1
  • weight time 2
  • weight change
  • sex

Issues

  • t-test on change vs. ancova
  • Statistician 1 concludes no difference in change
  • Statistician 2 concludes a difference in time 2 if controlling for time 1

Results

  • Both statisticians are correct
  • t-test on change = total effect
  • ancova = direct effect

DAG

Indirect effect: is a*c

Direct effect: b

Total effect: b + a*c - a

Treatment with confounding (Wainer & Brown)

Variables

  • weight time 1
  • weight time 2
  • weight change
  • table A vs. B

Issues

  • Heavier kids more likely to sit at table B
  • Two statisticians come the conclusions as before

Results

  • Weight time 1 is now a confounder
  • Arrow from time 1 to ‘treatment’
  • Statistician 1 is incorrect because they do not adjust
  • Statistician 2

Birth Weight Paradox

Variables

  • birthweight
  • smoking mom
  • infant mortality

Issues

  • No difference score
  • Before, focus on clash between two seemingly legitimate methods of analysis
  • Now using ancova but results seem implausible

Results

  • low birthweight children have higher mortality rate (100 fold higher)
  • children of smoking mothers notably more likely to have low birghtweight
  • low birthweight children born to smoking mothers have a lower mortality rate
  • Conclusion: expectant mothers should start smoking!

Results

Collider bias (explain away effect)

Explanation

Perspective 1

  • Controlling just for smoking leaves other causes, resulting in bias
  • Controlling for smoking changes the probability of other causes (due to BW collider) for any stratum of BW
  • Example: for BW=’low, if we compare smoking vs. non-smoking we are also comparing rare other causes vs. likely other causes

Perspective 2

  • Mediation context of previous: we want to know the mortality rate of babies e.g. smokers vs. non if BW controlled for
  • However here we have confounders, whereas before, the fundamental assumption was that there weren’t any.
  • Ajusting for BW doesn’t sever all paths traversing the mediator, and actually opens up a new path, and the effect is now spurious
  • For low BW, comparison of smoking vs. non-smoking compares no other causes vs. other causes